The Czech Republic midfielder scored the only goal of the game with a stunning strike in the second minute providing a valuable fillip to the Gunners' Premier League title push
Rosicky lashed home a spectacular half-volley after just 72 seconds to complete a third win in all competitions for Arsenal over their neighbours this term.
The victory moves Arsene Wenger's men to within four points of Chelsea with a game in hand after the leaders suffered a surprise reverse at Aston Villa on Saturday.
"It is a great result for us," Rosicky told Sky Sports. "These derby games are always very tough and it means a lot for us, obviously for our fans as well.
Discussing his stunning goal, Rosicky conceded there was a touch of fortune, with the ball falling perfectly into his path when Alex Oxlade-Chamberlain failed to control a return pass.
He said: "I just wanted to play Chambo through and his technique was not the best! After it bounced back to me, I just wanted to hit it. I just wanted to get it in at the far post. It was a great goal.
"It's one of my best, against Tottenham as well. I'm delighted by a goal like that and it is most important that we won the game."
The visitors came under sustained pressure in the second half as Tottenham sought a more direct route to goal, but Laurent Koscielny and Per Mertesacker excelled in repelling an attack spearheaded by ex-Arsenal striker Emmanuel Adebayor.
Koscielny said: "Adebayor is a very good player. It's difficult, he's good in the air.
"But I think we worked very hard. All the players who were on the pitch tried to give themselves for the team and for the win.
"With Per, we communicate very well on the pitch. It is very important for a centre-back.
"When we work very hard on the pitch we can win so we need to keep this for the end of the season."
Rosicky believes a thrilling title race will go down to the wire and refused to rule out Tottenham's chances of claiming a top-four berth despite their latest setback.
"I don't think you can count them out," he added. "This is a very tough league. Every game is very important and there are plenty of games to go so it will be very tough until the end."